Showing papers in "Bell System Technical Journal in 1948"

A mathematical theory of communication

Abstract: In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.

Spectra of quantized signals

Abstract: Signals which are quantized both in time of occurrence and in magnitude are in fact quite old in the communications art. Printing telegraph is an outstanding example. Here, time is divided into equal divisions, and the number of magnitudes to be distinguished in any one interval is usually no more than two, corresponding to the closed or open positions of a sending switch. It is only in recent years, however, that the development of high speed electronic devices has progressed sufficiently to enable quantizing techniques to be applied to rapidly changing signals such as produced by speech, music, or television. Quantizing of time, or time division, has found application as a means of multiplexing telephone channels.1 The method consists of connecting the different channels to the line in sequence by fast moving switches synchronized at the transmitting and receiving ends. In this way a transmission medium capable of handling a much wider band of frequencies than required for one telephone channel can be used simultaneously by a group of channels without mutual interference. The plan is the same as that used in multiplex telegraphy. The difference is that ordinary rotating machinery suffices at the relatively low speeds employed by the latter, while the high speeds needed for time division multiplex telephony can be realized only by practically inertialess electron streams. Also the widths of frequency band required for multiplex telephony are enormously greater than needed for the telegraph, and in fact have become technically feasible only with the development of wide-band radio and cable transmission systems. As far as any one channel is concerned the result is the same as in telegraphy, namely that signals are received at discrete or quantized times. In the limiting case when many channels are sent the speech voltage from one channel is practically constant during the brief switch closure and, in effect, we can send only one magnitude for each contact or quantum of time. The more familiar word “sampling” will be used here interchangeably with the rather formidable term “quantizing of time”.

Statistical properties of a sine wave plus random noise

Abstract: In Some technical problems we are concerned with a current which consists of a sinusoidal component plus a random noise component. A number of statistical properties of such a current are given here. The present paper may be regarded as an extension of Section 3.10 of an earlier paper,1 “Mathematical Analysis of Random Noise”, where some of the simpler properties of a sine wave plus random noise are discussed.

Metallic delay lenses

Abstract: A metallic lens antenna is described in which the focussing action is obtained by a reduction of the phase velocity of radio waves passing through the lens rather than by increasing it as in the original metal plate lens. The lens shape accordingly corresponds to that of a glass optical lens, being thick at the center and thin at the edges. The reduced velocity or “delay” is caused by the presence of conducting elements whose length in the direction of the electric vector of the impressed field is small compared to the wavelength; these act as small dipoles similar to the molecular dipoles set up in non-polar dielectrics by an impressed field. The lens possesses the relatively broad band characteristics of a solid dielectric lens, and since the conducting element can be made quite light, the weight advantage of the metal lens is retained. Various types of lenses are described and a theoretical discussion of the expected dielectric constants is given. An antenna design which is especially suitable for microwave repeater application is described in some detail.

The evolution of the quartz crystal clock

Abstract: Some of the earliest documents in human history relate to man's interest in timekeeping. This interest arose partly because of his curiosity about the visible world around him, and partly because the art of time measurement became an increasingly important part of living as the need for cooperation between the members of expanding groups increased. There are still in existence devices believed to have been made by the Egyptians six thousand years ago for the purpose of telling time from the stars, and there is good reason to believe that they were in quite general use by the better educated people of that period.1 Since that period there has been a continuous use and improvement of timekeeping methods and devices, following sometimes quite independent lines, but developing through a long series of new ideas and refinements into the very precise means at our disposal today.

Maximally-flat filters in waveguide

Abstract: Microwave radio relay repeaters require the use of band-pass filters which match closely the impedances of the interconnecting transmission lines and which suppress adjacent channels adequately. A type of structure culled a Maximally-Flat filter meets these requirements. The ladder network which gives a maximally-flat insertion loss characteristic is discussed and several methods of achieving its counterpart in microwave transmission lines are presented. Resonant cavities are used to simulate tuned circuits and the necessary formulas relative to this approximate equivalence are given. Experimental data confirm the theory and show that this technique yields remarkable impedance matches.

Potential coefficients for ground return circuits

Abstract: This paper is concerned with the effect of the finite conductivity and dielectric constant of the earth on the potential coefficient for a 1-wire ground return circuit. It has been customary to say that the potential coefficient V/Q is p 12 = c2 2 log ρ″/ρ′, elm units per cm. It is generally realized of course that this is just a good approximation to the true p 12 . To see that it is just an approximation one has only to imagine the earth turning into air, in which case the distance ρ″ will eventually cease to have significance. The object of this paper is to derive the complete expression for p 12 .

An experimental multichannel pulse code modulation system of toll quality

Abstract: Pulse Code Modulation offers attractive possibilities for multiplex telephony via such media as the microwave radio relay. The various problems involved in its use have been explored in terms of a 96-channel system designed to meet the transmission requirements commonly imposed upon commercial toll circuits. Twenty-four of the 96 channels have been fully equipped in an experimental model of the system. Coding and decoding devices are described, along with other circuit details. The coder is based upon a new electron beam tube, and is characterized by speed and simplicity as well as accuracy of coding. These qualities are matched in the decoder, which employs pulse excitation of a simple reactive network.

Electron beam deflection tube for pulse code modulation

Abstract: Pulse code transmission systems1 in which successive signal amplitude samples are transmitted by pulse code groups require special modulators. The essential operational requirements of a pulse code modulator are: (1) to quantize or measure the signal amplitude sample to the nearest step in the discrete amplitude scale transmitted by the pulse code system, and (2) to generate the group of on-off pulses identifying the step.

Reflections from circular bends in rectangular wave guides — Matrix theory

Abstract: A method of computing reflections produced by circular bends in rectangular wave guides is presented. The procedure employs the theory of matrices. Although the matrix equations are quite simple, a considerable amount of calculation is necessary before quantitative results may be obtained. Fortunately, the approximate formulas pertaining to gentle bends hold surprisingly well for rather sharp bends. These formulas are obtained by a limiting process from the matrix equations. The approximate formula for reflection from an H-bend (in which the magnetic vector lies in the plane of the bend) generalizes an earlier result due to R. E. Marshak. The corresponding formula for the E-bend appears to be new.

Microwave repeater research

Abstract: It was some 80 years ago that Maxwell and Hertz demonstrated that free space is a good transmission medium for electromagnetic waves. Since this fundamental contribution, the radio art has advanced tremendously and a decade ago it had progressed to the point where it was possible to construct equipment suitable for quantitative propagation studies of microwaves. Such studies were made and they indicated that normal propagation over “line-of-sight” paths of signals of 10 to 20 centimeters wavelength was characterized by free space attenuation and freedom from atmospheric interference. These results, together with the facts that in this wavelength range wide bands of frequencies are available and it is possible to design small antennas having high directivity, encouraged us to start more comprehensive research work on microwave repeater circuits. This paper gives the present status of the work which was interrupted by our war efforts and resumed at the end of the war with the construction of an experimental New York-Boston system as an initial objective.

Equivalent circuits of linear active four-terminal networks

Abstract: The art of equivalent network representation has grown very considerably since its inception by Dr G A Campbell In his paper “Cissoidal Oscillations” which was published in 1911 he proved that any passive network made up of a finite number of invariable elements and having one pair of input terminals and one pair of output terminals is externally equivalent to an unsymmetrical T or II network From this modest beginning the field of applications of the equivalent circuit concept has steadily expanded so that by now the whole field of linear passive circuit theory has been subjected to equivalent circuit interpretation

A non-reflecting branching filter for microwaves

Abstract: Microwave branching filters are required as integral parts of multi-channel microwave radio relay systems. These filters must have characteristics which are difficult to attain if one attempts to extend familiar lower frequency techniques to the microwave region. A novel network configuration, through which currently anticipated requirements can be met without excessive difficulty, is described in this paper. In this configuration individual constant resistance channel dropping units are formed of appropriate assemblies of two hybrid circuits, two band reflection filters and two quarter wavelengths of line. An assembly of N channel dropping units in cascade then forms an N channel constant resistance branching network. The mechanical and electrical characteristics of a practical five channel branching filter of this type are described. As a result of experience with this prototype filter it can be stated with some safety that these requirements can he fulfilled with a network of this type. Experimentally observed impedance, insertion loss and phase characteristics were fully satisfactory. In addition the circuit appears to be flexible enough both electrically and mechanically to fulfill the various types of systems needs which may be encountered at branch points or when channels must be added or interchanged.

Methods of electromagnetic field analysis

Abstract: This paper presents a discussion of ideas involved in various mathematical methods of electromagnetic field analysis and of the inter-relations between these ideas. It stresses the points of contact between circuit and field theories and their mutually complementary character. While the field theory focuses our attention on the electromagnetic state as a function of position in space, the generalized circuit theory is preoccupied with the electromagnetic state as a function of time. The points of contact between the field and circuit theories are many. Thus, Maxwell's equations are identical with Kirchhoff's equations (really Lagrange-Maxwell equations) of certain three-dimensional networks in which only the adjacent meshes are coupled. The integral equations for the electrical current in conductors embedded in dielectric media are also Kirchhoff equations of certain networks containing infinitely many meshes with a coupling between every two meshes. From the point of view of electrical performance the difference between a physical network of lumped elements and a continuous network, such as a resonator, is due to a certain difference in the distribution of the zeros and poles of associated impedance functions in the complex impedance plane. Similarly, the difference between ordinary transmission lines and wave guides is due to a difference in the distribution o(natural propagation constants. The paper ends with a general discussion of the discontinuities in wave guides, idealized boundary conditions for simplification of electromagnetic problems, and the analytical character of field vectors regarded as functions of the complex oscillation constant.

An aspect of the dialing behavior of subscribers and its effect on the trunk plant

Abstract: During the war it became necessary for the Hell System Companies to lower many service standards. Among these was the standard for the provision of trunks for handling subscriber-dialed calls. In the interest of economy the number of trunks for a given volume of traffic was lowered. It is evident that for any given case there is a lower limit to the number of trunks that should be provided for handling subscriber-dialed calls. Below this limit congestion of calls gets beyond control. The control of congestion is important. In the case of operator-handled calls it is possible to control congestion by filing tickets and placing calls in an orderly fashion. In the case of subscriber-dialed calls the subscriber may with impunity make many, indeed very many, successive dialing attempts to complete a call that is blocked due to a shortage of trunks. If, in a particular office enough subscribers do this simultaneously, a sender shortage may develop with its resulting reaction on the whole office.

The measurement of delay distortion in microwave repeaters

Abstract: Measuring equipment is described which is capable of measuring delay distortion of the order of 10−9 seconds in a wide band microwave television relay repeater. Two measuring circuits are discussed. The first is a circuit for measuring the relative phase shift versus frequency from which the delay distortion may be computed. The second circuit gives the delay directly from a single measurement. The measuring equipment is designed to work in the intermediate frequency range from 50 to 80 megacycles, but by applying suitable conversion equipment measurements can be made at microwave frequencies.

Noise in resistances and electron streams

Abstract: Technically correct results in a field are achieved initially in diverse and often confusing and complicated ways. Sometimes, such results are later brought together to give them a more unified form and a sounder basis; such critical summary and exposition is of great value. In quite another way, a worker who uses results established in a field will discover many plausible reasons for believing the results, and he will find eventually that an air of inevitability and “understanding” pervades the subject. Such “understanding” is not to be confused with the process of rigorous proof carried out step by step, but it can help in organizing and making use of a body of related material.

A note on a parallel-tuned transformer design

Abstract: An analysis of the parallel-tuned transformer used in radio-frequency amplifiers has been made for a slightly over-coupled case. The resulting design formulas are simple and practical. Two cases are discussed: (a) the so-called matched transformer, with resistance loading on each side; (b) a transformer with loading on one side only, which has the same pass-band and phase characteristics as the matched transformer, but gives 3 db more gain when used as an in terstage. A special arrangement of (a) where the matched transformer design is used with one resistor removed, giving a transformer witha considerably double-humped pass-band characteristic and about 6 dh more gain, is also discussed.

The approximate solution of linear differential equations

Abstract: Linear differential equations with variable coefficients occur in many fields of applied mathematics: in the theories of acoustics, elastic waves, electromagnetic waves in stratified media, nonuniform transmission lines, wave guides, antennas, wave mechanics. The “Wave Perturbation” method described in greater detail elsewhere1 is particularly useful in those ranges of the independent variable in which the “WKB Approximation” is not sufficiently accurate. The present paper endeavors to illustrate the remarkable accuracy of this method, particularly when compared with Picard's method.

Transverse fields in traveling-wave tubes

Abstract: Traveling-wave tubes will have gain even if the r-f field at the mean position of the electron stream is purely transverse. The addition of a longitudinal magnetic focusing field reduces the gain due to transverse fields and increases the electron velocity for optimum gain.

Transients in mechanical systems

Abstract: A study of the response of an electrical network or system to the input of transients in the form of short-duration pulses is an accepted method of analysis of the network. By comparing the input and the output, conclusions may be drawn as to the respective merit of the various components. Until recently similar procedures were only of academic interest with mechanical systems. However, the tests for mechanical ruggedness, which are required of electronic gear in order to pass specifications for the armed forces, are an example of the application of transients to a mechanical system. These tests are known as High Impact Shock Tests.

Analysis and performance of waveguide-hybrid rings for microwaves

Abstract: This paper presents an analytical treatment of waveguide hybrid rings for microwaves, considered as re-entrant transmission lines. The resulting lines are transformed into equivalent “T” or “lattice” network sections, and determinantal methods are applied in analyzing these equivalent network assemblies for their transmission properties. Some experimental results obtained from a carefully constructed sample of each of two specific types are given. A satisfactory agreement is obtained between the values predicted by theory and experimental results.

Frequency shift telegraphy-radio and wire applications

Abstract: Frequency shift telegraphy is described and compared with amplitude modulation telegraphy under various conditions found in radio and wire transmission. Experimental data are given to demonstrate the influence of various design factors on the over-all performance under these conditions. It is shown that the most outstanding characteristic of the frequency shift method is its ability to accept large and rapid changes in signal amplitude. Frequency shift telegraphy thus proves to be of great advantage for use in the H.F. radio range. Frequency shift telegraphy also shows an advantage over amplitude modulation telegraphy with respect to noise. For applications where the level variations are small or slow the advantage of the frequency shift method over amplitude modulation is relatively small.

Transient response of an FM receiver

Abstract: This paper develops various formulas for the response of an FM receiver to signal or noise input voltages of arbitrary form. The principal object in view is to obtain a more complete understanding of how an FM receiver responds to transient voltages, such as those arising from ignition interference, but the more general aspects of the theory have other applications as well. In particular, general formulas are given for the response of a linear circuit to an applied voltage, or current, of variable frequency. The Fourier transforms, or frequency spectra, of the response, and the envelope thereof, are determined.